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Answer 1

so, your question is solved above

Answer 2

$Given : \frac{3}{5 - \sqrt{3} } + \frac{2}{5 + \sqrt{3} }$

After rationalizing the denominators, We get

$= \ \textgreater \ \frac{3}{5 - \sqrt{3} } * \frac{5 + \sqrt{3} }{5 + \sqrt{3} } + \frac{2}{5 + \sqrt{3} } * \frac{5 - \sqrt{3} }{5 - \sqrt{3} }$

$= \ \textgreater \ \frac{3(5 + \sqrt{3}) }{(5 + \sqrt{3})(5 - \sqrt{3}) } + \frac{2(5 - \sqrt{3}) }{(5 + \sqrt{3})(5 - \sqrt{3} )}$

$= \ \textgreater \ \frac{3(5 + \sqrt{3} ) + 2(5 - \sqrt{3}) }{(5 + \sqrt{3} (5 - \sqrt{3}) }$

$= \ \textgreater \ \frac{15 + 3 \sqrt{3}+ 10 - 2 \sqrt{3} }{5^2 - ( \sqrt{3} )^2 }$

$= \ \textgreater \ \frac{25 + \sqrt{3} }{25 - 3}$

$= \ \textgreater \ \frac{25 + \sqrt{3} }{22}$



Hope this helps!